270 likes | 384 Vues
Assigned Groups. Find which group you’re in Find where it is Sit there Be friendly. 7. 8. 4. 5. 6. 1. 2. 3. screen. screen. Announcements. Show your name tags ! Please give Moodle your registered name Labs and discussions have already started. Standard.
E N D
Assigned Groups • Find which group you’re in • Find where it is • Sit there • Be friendly 7 8 4 5 6 1 2 3 screen screen
Announcements • Show your name tags! • Please give Moodle your registered name • Labsanddiscussionshavealreadystarted
Standard • Relate distance, velocity, and acceleration mathematically, graphically, and conceptually. Objectives • Relate distance, velocity, and acceleration. • Interpret distance-time, velocity-time, and acceleration-time plots.
Describing Motion It’s all math today
The Tortoise and the Hare Told in words, formulas, and graphs
Question Who was faster? • The tortoise. • The hare. • They had the same speed. • What do you mean by faster?
Group Work: Graph Describe the Tortoise-and-hare race using a position-time graph. • Same axes • One world-line for tortoise, another for hare • Indicate significant times and positions
Dd average speed = over entire interval Dt Dd instantaneous speed = lim at one instant Dt t 0 Speed Rate of changing position
Speed as Slope D distance Speed = = slope of graph! D time distance Dd Dt time
Question Who had the highest average speed? • The tortoise. • The hare. • Their average speeds were the same. • Over what time interval?
Poll Question Who had the highest instantaneous speed? • The tortoise. • The hare. • Their instantaneousspeeds were the same. • At what time?
Speed Units distance = m/s time
Group Work: Graph Describe the Tortoise-and-hare race using a velocity-time graph.
hare tortoise Distance Change as Area • What are the areas under the tortoise’s and hare’s velocity-time plots? area = vDt = D(distance) speed t0 t1 t2 t3 t4 time
Group Work: Graph A car waits at a stop light for 5 seconds, smoothly accelerates to 15 m/s over 5 seconds, and then continues at 15 m/s. Describe the car’s motion using a velocity-time graph.
Dv average acceleration = Dt over the entire interval t 0 Dv instantaneous acceleration = lim Dt at one instant Acceleration Rate of changing velocity
velocity m/s s time Acceleration Units = = m/s2
Group Work: Graph What is the car’s acceleration at the different times? Describe the car’s motion using an acceleration-time graph.
Group Work: Compute How far does the car travel: • Between 0 s and 5 s? • Between 10 s and 15 s?
slope = velocity d t slope = acceleration v area = distance t a area = velocity t Acceleration Starting from a traffic light that turns green
Group Work 7 Describe four ways (x-t, v-t, a-t, words): position 0 time
Group Work 7 Describe four ways (x-t, v-t, a-t, words): velocity 0 time
Group Work 7 Describe four ways (x-t, v-t, a-t, words): acceleration 0 time
Group Work 7 A coconut hangs motionless from its tree, then drops with increasing downward speed until it lands on the ground, quickly coming to rest. Describe four ways (x-t, v-t, a-t, words):
Formulas for Constant Acceleration • Velocity change Dv=aDt • Velocity vt = v0 + Dv = v0 + aDt • Position change Dx = v0 Dt + 1/2 a (Dt)2 • Position xt = x0 + v0 Dt + 1/2 a (Dt)2
Reading for Next Time • Vectors: how we handle quantities with directions • Important vectors: position, velocity, acceleration, force